Your experiment sounds interesting. Have you also considered the impact of
which cards the children might choose, independent of the mastery rate with the
different types of cards?

I would personally be interested to see if there are different voice inflections
or visual responses to your daughter's answers when presented with the pink
cards, i.e., will the difference in color, or the presence of a picture, change
her participation in the moment in any way, change her experience of doing the
exercises. How to explain this, if she is processing the information
differently, there might (I want to say should) be some evidence of this in
bodily responses.

Let me pass another situation by you, again with the whiteboarded tables, but
this time, with children in a home situation. An older sister and a younger
sister, both from Mexico, older sister is doing well in school, including math,
about 10 years old; younger sister was about 8 years old, having a difficult
time in school, including math, couldn't do simple problems like addition. When
I got a whiteboard out and set it on the kitchen table (it wasn't corner to
corner coverage like the tutor center tables, but just a good sized piece of
whiteboard set on the table), I worked with the girls individually. The older
girl did well no matter what, so the board didn't serve any overriding purpose
with her, however, when the younger child was drawing pictures on the board, she
began verbally spouting out answers to her sister's higher level math problems.
How it all played out in her head, I have no idea, except that while she was
actively engaged and focused on drawing pictures, her brain was able to function
very adequately in some kind of a background mode on math. This child seemed to
be swathed in learning disabilities, and I say this based upon opinion only. I
wasn't even at the house to work with the children on their math, but was
visiting because they are very extended family on my ex-husband's side of the
family at the same time I was experimenting around with the effects of a
whiteboard writing surface. Everything about the visit was coincidence. I
didn't follow up with this child having nothing to back up my ideas, and her
situation seemed to be so complex, she was expected to underperform by the
family, who treated her in a most loving and "understanding" way, and all the
time I felt that there was anything but understanding going on with this child,
that under the surface there was a great deal to deal with.

What I have become convinced of, though, in my sporadic dealings with children,
is that rigidity and conformity is going to necessarily leave some children out,
and that approaches should be as fluid as possible so they can take different
forms with different children, and the unexpected has room to take place.

However it is that your children react to the different forms of the flash cards
you put before them, mastery will probably be only one indicator, and likely not
the most important one, unless the only standard of value is a
results-oriented one.

This material is based upon work supported by the
National Science Foundation under Grant DUE-0226284.
Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the
National Science Foundation.